TSTP Solution File: SET069+1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET069+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:52:56 EDT 2024
% Result : Theorem 11.47s 1.93s
% Output : CNFRefutation 11.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 139 ( 47 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 134 ( 46 ~; 64 |; 16 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 6 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X1,X2)
& subclass(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(pair_contains_only_other2,conjecture,
! [X1,X2] :
( ~ member(X2,universal_class)
=> unordered_pair(X1,X2) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_contains_only_other2) ).
fof(c_0_7,plain,
! [X24,X25,X26] :
( ( member(X24,universal_class)
| ~ member(X24,unordered_pair(X25,X26)) )
& ( X24 = X25
| X24 = X26
| ~ member(X24,unordered_pair(X25,X26)) )
& ( X24 != X25
| ~ member(X24,universal_class)
| member(X24,unordered_pair(X25,X26)) )
& ( X24 != X26
| ~ member(X24,universal_class)
| member(X24,unordered_pair(X25,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])])]) ).
fof(c_0_8,plain,
! [X12] : singleton(X12) = unordered_pair(X12,X12),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_9,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X29,X30,X31,X32,X33] :
( ( ~ subclass(X29,X30)
| ~ member(X31,X29)
| member(X31,X30) )
& ( member(esk3_2(X32,X33),X32)
| subclass(X32,X33) )
& ( ~ member(esk3_2(X32,X33),X33)
| subclass(X32,X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subclass_defn])])])])])])]) ).
fof(c_0_12,plain,
! [X39] : subclass(X39,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
cnf(c_0_13,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(esk3_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[regularity]) ).
fof(c_0_18,plain,
! [X89,X90] :
( ( subclass(X89,X90)
| X89 != X90 )
& ( subclass(X90,X89)
| X89 != X90 )
& ( ~ subclass(X89,X90)
| ~ subclass(X90,X89)
| X89 = X90 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])])]) ).
cnf(c_0_19,plain,
( subclass(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( esk3_2(singleton(X1),X2) = X1
| subclass(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( esk3_2(unordered_pair(X1,X2),X3) = X2
| esk3_2(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
fof(c_0_23,plain,
! [X63] :
( ( member(esk5_1(X63),universal_class)
| X63 = null_class )
& ( member(esk5_1(X63),X63)
| X63 = null_class )
& ( disjoint(esk5_1(X63),X63)
| X63 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( subclass(singleton(X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( member(esk3_2(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_27,plain,
( esk3_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_28,plain,
( member(esk5_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( X1 = singleton(X2)
| ~ member(X2,X1)
| ~ subclass(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( member(X1,universal_class)
| subclass(unordered_pair(X2,X1),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X2] :
( ~ member(X2,universal_class)
=> unordered_pair(X1,X2) = singleton(X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[pair_contains_only_other2])]) ).
cnf(c_0_34,plain,
( member(esk5_1(X1),universal_class)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
( esk5_1(unordered_pair(X1,X2)) = X2
| esk5_1(unordered_pair(X1,X2)) = X1
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_9,c_0_28]) ).
cnf(c_0_36,plain,
( unordered_pair(X1,X2) = singleton(X3)
| member(X2,universal_class)
| ~ member(X3,unordered_pair(X1,X2))
| ~ member(X1,singleton(X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_32]) ).
fof(c_0_39,negated_conjecture,
( ~ member(esk2_0,universal_class)
& unordered_pair(esk1_0,esk2_0) != singleton(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_40,plain,
( esk5_1(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( esk5_1(singleton(X1)) = X1
| singleton(X1) = null_class ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_42,plain,
( unordered_pair(X1,X2) = singleton(X1)
| member(X2,universal_class)
| ~ member(X1,singleton(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_21]) ).
cnf(c_0_43,plain,
( member(X1,singleton(X1))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_38,c_0_10]) ).
cnf(c_0_44,negated_conjecture,
unordered_pair(esk1_0,esk2_0) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
~ member(esk2_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( singleton(X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_48,plain,
( unordered_pair(X1,X2) = singleton(X1)
| member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
member(esk1_0,universal_class),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_48]),c_0_49])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET069+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.37 % Computer : n014.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon May 20 11:04:38 EDT 2024
% 0.13/0.37 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.47/1.93 # Version: 3.1.0
% 11.47/1.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 11.47/1.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.47/1.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.47/1.93 # Starting new_bool_3 with 300s (1) cores
% 11.47/1.93 # Starting new_bool_1 with 300s (1) cores
% 11.47/1.93 # Starting sh5l with 300s (1) cores
% 11.47/1.93 # sh5l with pid 19807 completed with status 0
% 11.47/1.93 # Result found by sh5l
% 11.47/1.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 11.47/1.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.47/1.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.47/1.93 # Starting new_bool_3 with 300s (1) cores
% 11.47/1.93 # Starting new_bool_1 with 300s (1) cores
% 11.47/1.93 # Starting sh5l with 300s (1) cores
% 11.47/1.93 # SinE strategy is gf500_gu_R04_F100_L20000
% 11.47/1.93 # Search class: FGHSM-FFMS31-MFFFFFNN
% 11.47/1.93 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 11.47/1.93 # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 130s (1) cores
% 11.47/1.93 # G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 19810 completed with status 0
% 11.47/1.93 # Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 11.47/1.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 11.47/1.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.47/1.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.47/1.93 # Starting new_bool_3 with 300s (1) cores
% 11.47/1.93 # Starting new_bool_1 with 300s (1) cores
% 11.47/1.93 # Starting sh5l with 300s (1) cores
% 11.47/1.93 # SinE strategy is gf500_gu_R04_F100_L20000
% 11.47/1.93 # Search class: FGHSM-FFMS31-MFFFFFNN
% 11.47/1.93 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 11.47/1.93 # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 130s (1) cores
% 11.47/1.93 # Preprocessing time : 0.002 s
% 11.47/1.93
% 11.47/1.93 # Proof found!
% 11.47/1.93 # SZS status Theorem
% 11.47/1.93 # SZS output start CNFRefutation
% See solution above
% 11.47/1.93 # Parsed axioms : 44
% 11.47/1.93 # Removed by relevancy pruning/SinE : 3
% 11.47/1.93 # Initial clauses : 84
% 11.47/1.93 # Removed in clause preprocessing : 0
% 11.47/1.93 # Initial clauses in saturation : 84
% 11.47/1.93 # Processed clauses : 3889
% 11.47/1.93 # ...of these trivial : 57
% 11.47/1.93 # ...subsumed : 2665
% 11.47/1.93 # ...remaining for further processing : 1167
% 11.47/1.93 # Other redundant clauses eliminated : 51
% 11.47/1.93 # Clauses deleted for lack of memory : 0
% 11.47/1.93 # Backward-subsumed : 20
% 11.47/1.93 # Backward-rewritten : 85
% 11.47/1.93 # Generated clauses : 83733
% 11.47/1.93 # ...of the previous two non-redundant : 78270
% 11.47/1.93 # ...aggressively subsumed : 0
% 11.47/1.93 # Contextual simplify-reflections : 30
% 11.47/1.93 # Paramodulations : 83496
% 11.47/1.93 # Factorizations : 184
% 11.47/1.93 # NegExts : 0
% 11.47/1.93 # Equation resolutions : 53
% 11.47/1.93 # Disequality decompositions : 0
% 11.47/1.93 # Total rewrite steps : 33103
% 11.47/1.93 # ...of those cached : 32491
% 11.47/1.93 # Propositional unsat checks : 0
% 11.47/1.93 # Propositional check models : 0
% 11.47/1.93 # Propositional check unsatisfiable : 0
% 11.47/1.93 # Propositional clauses : 0
% 11.47/1.93 # Propositional clauses after purity: 0
% 11.47/1.93 # Propositional unsat core size : 0
% 11.47/1.93 # Propositional preprocessing time : 0.000
% 11.47/1.93 # Propositional encoding time : 0.000
% 11.47/1.93 # Propositional solver time : 0.000
% 11.47/1.93 # Success case prop preproc time : 0.000
% 11.47/1.93 # Success case prop encoding time : 0.000
% 11.47/1.93 # Success case prop solver time : 0.000
% 11.47/1.93 # Current number of processed clauses : 1058
% 11.47/1.93 # Positive orientable unit clauses : 89
% 11.47/1.93 # Positive unorientable unit clauses: 1
% 11.47/1.93 # Negative unit clauses : 25
% 11.47/1.93 # Non-unit-clauses : 943
% 11.47/1.93 # Current number of unprocessed clauses: 74279
% 11.47/1.93 # ...number of literals in the above : 266623
% 11.47/1.93 # Current number of archived formulas : 0
% 11.47/1.93 # Current number of archived clauses : 105
% 11.47/1.93 # Clause-clause subsumption calls (NU) : 136288
% 11.47/1.93 # Rec. Clause-clause subsumption calls : 94348
% 11.47/1.93 # Non-unit clause-clause subsumptions : 1720
% 11.47/1.93 # Unit Clause-clause subsumption calls : 5027
% 11.47/1.93 # Rewrite failures with RHS unbound : 0
% 11.47/1.93 # BW rewrite match attempts : 170
% 11.47/1.93 # BW rewrite match successes : 26
% 11.47/1.93 # Condensation attempts : 0
% 11.47/1.93 # Condensation successes : 0
% 11.47/1.93 # Termbank termtop insertions : 1650759
% 11.47/1.93 # Search garbage collected termcells : 927
% 11.47/1.93
% 11.47/1.93 # -------------------------------------------------
% 11.47/1.93 # User time : 1.335 s
% 11.47/1.93 # System time : 0.064 s
% 11.47/1.93 # Total time : 1.399 s
% 11.47/1.93 # Maximum resident set size: 1924 pages
% 11.47/1.93
% 11.47/1.93 # -------------------------------------------------
% 11.47/1.93 # User time : 1.336 s
% 11.47/1.93 # System time : 0.067 s
% 11.47/1.93 # Total time : 1.403 s
% 11.47/1.93 # Maximum resident set size: 1760 pages
% 11.47/1.93 % E---3.1 exiting
% 11.47/1.93 % E exiting
%------------------------------------------------------------------------------